docs: def C_long_radius_nozzle(D, Do, rho, mu, m):
      r'''Calculates the coefficient of discharge of a long radius nozzle used
      for measuring flow rate of fluid, based on the geometry of the nozzle, 
      mass flow rate through the nozzle, and the density and viscosity of the
      fluid.
      
      .. math::
          C = 0.9965 - 0.00653\beta^{0.5} \left(\frac{10^6}{Re_D}\right)^{0.5}
          
      Parameters
      ----------
      D : float
          Upstream internal pipe diameter, [m]
      Do : float
          Diameter of long radius nozzle orifice at flow conditions, [m]
      rho : float
          Density of fluid at `P1`, [kg/m^3]
      mu : float
          Viscosity of fluid at `P1`, [Pa*s]
      m : float
          Mass flow rate of fluid through the nozzle, [kg/s]
          
      Returns
      -------
      C : float
          Coefficient of discharge of the long radius nozzle orifice, [-]
  
      Notes
      -----
      
      Examples
      --------
      >>> C_long_radius_nozzle(D=0.07391, Do=0.0422, rho=1.2, mu=1.8E-5, m=0.1)
      0.9805503704679863
      
      References
      ----------
      .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
         Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
      .. [2] ISO 5167-3:2003 - Measurement of Fluid Flow by Means of Pressure 
         Differential Devices Inserted in Circular Cross-Section Conduits Running
         Full -- Part 3: Nozzles and Venturi Nozzles.
      '''
      A_pipe = pi/4.*D*D
      v = m/(A_pipe*rho)
      Re_D = rho*v*D/mu
      beta = Do/D
      return 0.9965 - 0.00653*beta**0.5*(1E6/Re_D)**0.5